How to explain Bell's theorem to non-scientists

[edfriedmanis65]

How did you find PF?: Wandering on the internet looking for answers about Bell's theorem

I teach adult education at 2 universities near Denver and I'm writing a book for non-scientists interested in quantum mechanics and its foundations. The challenge is to present the concepts digestibly without resorting to mathematics. Of course, one of the key topics in quantum is Bell's theorem so I have worked hard to provide my students with a vision of what Bell was talking about without forcing them to go through the bras and kets that are common in quantum mechanics books, even the ones for undergraduates.

So, I am always looking for analogies and compelling artwork to help me create instructional materials that will work for my senior citizen students. Perhaps you have comments on the approach I have attached.

 

[.Scott]

To communicate the gist of the Bell inequality, I say this:

If A and B are only 10 percent different from each other, and B and C are only 10 percent different from each other, then it should not be possible for A and C to be more than 20 percent different from each other. But when the measurements are made, that's the kind of thing that's being seen. So there's some kind of "cheating" going on - somehow the choice of measurements is affecting what is being measured.

 

[pines-demon]

I have tried to provide a popular version of Bell's inequalities many times and have found that if the students are not willing to go through the derivation of the inequalities they will not get it. The best is to retort to simplified versions like the Mermin's device which gives the best gist of the problem, however even in that case you need students to have time to look at the tables in Mermin's problem and that requires a minima of math. Other versions require making a Venn diagram, but again you have to construct it and analyze it. I think it is impossible to tell Bell's inequality in the passing (in 5 min or so) without creating many misconceptions.

Edit: looking at your document, I think you can build a proof in the way that you are trying to do, however I feel that doing that on smokers surveys abstracts the problem away from physics. Mermin's version is at least better in the sense that you can discuss important conditions like locality.

Edit: Also be careful on what you are saying about realism and locality, it seems very shallow and possibly wrong, many people imply many things by those two terms. What is your target audience?

 

[PeterDonis]

Moderator's note: Thread moved to the education forum.

 

[PeterDonis]

Let me take a stab at a brief description of what the Bell inequalities, or more precisely experimentally observed violations of them, mean.

We have two objects that are prepared at a common source and then separated, and measurements are made on them separately. The measurements are made at spacelike separated events, so it is impossible for even a light signal to transmit information about one measurement result to the other measurement. The measurements are of some observable that can vary in direction, and the objects can be prepared so that if both are measured in the same direction, the results are perfectly correlated (or anti-correlated, it doesn't matter which).

The Bell inequalities are inequalities that set limits on how correlated (or anti-correlated) the two measurements can be if they are made in different directions, if we make two assumptions:

(1) The measurement results for both objects for all possible directions of measurement are determined in advance, but the predetermined results are not in general knowable by the experimenter, hence the term "hidden variables";

(2) Each object's measurement result depends only on the "hidden variables" and the direction in which it is measured; it does not depend on the direction in which the other object is measured.

When we set up such scenarios with classical objects, like pairs of socks, pairs of shoes, etc., we find that the Bell inequalities are never violated. However, if we do it with quantum objects that are entangled, like pairs of entangled photons or pairs of entangled electrons, we find that the Bell inequalities are violated. That means that for such objects, at least one of the two assumptions given above is not valid. In other words, either (1) or (2) above is not true. But either of those presents an intuitive problem:

If (1) is not true, then it seems impossible to understand how the perfect correlations (or anti-correlations) can be enforced when the measurements are in the same direction;

If (2) is not true, then it seems that somehow the measurements must be able to "communicate" with each other so that the results can depend on both measurement directions; but this "communication" must happen faster than light, hence Einstein's term "spooky action at a distance".

 

[haushofer]

I really like the paper "The mystery of the quantum cakes" by Kwiat and Hardy. Freely available online. What better analogy to use than cakes. ;)

If you don't like cakes, you can use socks, like Bell did in "Bertlmann's Socks and the Nature of Reality." Also freely available.

 

[pines-demon]

If you don't like cakes, you can use socks, like Bell did in "Bertlmann's Socks and the Nature of Reality." Also freely available.

I like Bell but I do not like that particular explanation of his (it is a technical as the proof itself). I would prefer to stick to cakes, taste better.

 

[Andy Resnick]

How did you find PF?: Wandering on the internet looking for answers about Bell's theorem

I teach adult education at 2 universities near Denver and I'm writing a book for non-scientists interested in quantum mechanics and its foundations. The challenge is to present the concepts digestibly without resorting to mathematics. Of course, one of the key topics in quantum is Bell's theorem so I have worked hard to provide my students with a vision of what Bell was talking about without forcing them to go through the bras and kets that are common in quantum mechanics books, even the ones for undergraduates.

So, I am always looking for analogies and compelling artwork to help me create instructional materials that will work for my senior citizen students. Perhaps you have comments on the approach I have attached.

When I discuss this topic in class (undergrad quantum), I make the case that the entangled objects (two correlated photons, two correlated electrons, two correlated particles) are not actually two distinct objects, but rather a single object. The initial context is Young's double slit experiment, but later I discuss type-II parametric down-conversion.

When students look perplexed about 'nonlocal' issues, I describe the wave generated by throwing a rock into water and then ask "where is the wave?"

 

[pines-demon]

The initial context is Young's double slit experiment, but later I discuss type-II parametric down-conversion.

When students look perplexed about 'nonlocal' issues, I describe the wave generated by throwing a rock into water and then ask "where is the wave?"

These are two different issues to understand in quantum mechanics, one is how to explain superposition and interference ($n\geq1$) and the other is entanglement ($n>1$).

 

[Andy Resnick]

These are two different issues to understand in quantum mechanics, one is how to explain superposition and interference ($n\geq1$) and the other is entanglement ($n>1$).

But they are both related by the concept of 'coherence', so by teaching one, you can easily discuss the other. Wolf and Mandel's "Optical Coherence and Quantum Optics" is a good reference.

 

[pines-demon]

But they are both related by the concept of 'coherence', so by teaching one, you can easily discuss the other. Wolf and Mandel's "Optical Coherence and Quantum Optics" is a good reference.

Sure but one can be simulated classically while the other (entanglement) cannot, that's why it is so hard to make a simple mental image to explain it.

 

[Andy Resnick]

Sure but one can be simulated classically while the other (entanglement) cannot, that's why it is so hard to make a simple mental image to explain it.

Since the OP has never chimed in, it's not clear we are helping.